{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:35:28Z","timestamp":1760146528984,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T00:00:00Z","timestamp":1731542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Centre for Mathematics of the University of Coimbra","award":["FQM298","ProyExcel_00780"],"award-info":[{"award-number":["FQM298","ProyExcel_00780"]}]},{"name":"PCI of the UCA \u2018Teor\u00eda de Lie y Teor\u00eda de Espacios de Banach\u2019","award":["FQM298","ProyExcel_00780"],"award-info":[{"award-number":["FQM298","ProyExcel_00780"]}]},{"name":"Regional Government of Andalusia, Spain","award":["FQM298","ProyExcel_00780"],"award-info":[{"award-number":["FQM298","ProyExcel_00780"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we present some generalizations of Jacobi\u2013Jordan algebras. More concretely, we will focus on noncommutative Jacobi\u2013Jordan algebras, Malcev\u2013Jordan algebras, and general Jacobi\u2013Jordan algebras. We adapt a method, used to classify Poisson algebras, in order to classify all general Jacobi\u2013Jordan algebras up to dimension 4, and, in particular, all noncommutative Jacobi\u2013Jordan algebras up to dimension 4. We present the classification of Malcev\u2013Jordan algebras up to dimension 5. As the class of Jacobi\u2013Jordan algebras (commutative algebras that satisfy the Jacobi identity), we find that Malcev\u2013Jordan algebras are Jordan algebras but not necessarily nilpotent. However, we show that the classification of nilpotent Malcev\u2013Jordan algebras is sufficient to obtain the classification of the whole class.<\/jats:p>","DOI":"10.3390\/axioms13110787","type":"journal-article","created":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T09:14:31Z","timestamp":1731575671000},"page":"787","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Generalizations of Jacobi\u2013Jordan Algebras"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2149-0569","authenticated-orcid":false,"given":"Hani","family":"Abdelwahab","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"given":"Naglaa Fathi","family":"Abdo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1369-3737","authenticated-orcid":false,"given":"Elisabete","family":"Barreiro","sequence":"additional","affiliation":[{"name":"CMUC, Department of Mathematics, FCTUC, University of Coimbra, Largo D. Dinis, 3000-143 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4842-6735","authenticated-orcid":false,"given":"Jos\u00e9 Mar\u00eda","family":"S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of C\u00e1diz, 11519 Puerto Real, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1090\/S0002-9947-1948-0027750-7","article-title":"Power-associative rings","volume":"64","author":"Albert","year":"1948","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_2","first-page":"A566","article-title":"A counterexample to a conjecture of Albert","volume":"19","author":"Suttles","year":"1972","journal-title":"Not. Am. Math. 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Algebra Appl."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/11\/787\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:32:26Z","timestamp":1760113946000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/11\/787"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,14]]},"references-count":16,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["axioms13110787"],"URL":"https:\/\/doi.org\/10.3390\/axioms13110787","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,11,14]]}}}